The goals of the `factorial2x2`

package are twofold: First, to provide power calculations for a two-by-two factorial design in which the effects of the two factors may be sub-additive. Power is provided for the overall effect test for as well as the multiple testing procedures described in Leifer, Troendle, Kolecki, and Follmann (2020). Second, to analyze two-by-two factorial trial data which may include baseline adjustment covariates. Further details are described in the factorial2x2 vignette.

You can install the released version of factorial2x2 from CRAN with:

We reproduce the power calculations for scenario 4 from Table 2 in Leifer, Troendle, et al. using the `fac2x2design`

function.

```
n <- 4600 # total sample size
rateC <- 0.0445 # one year event rate in the control group
hrA <- 0.80 # simple A effect hazard ratio
hrB <- 0.80 # simple B effect hazard ratio
hrAB <- 0.72 # simple AB effect hazard ratio
mincens <- 4.0 # minimum censoring time in years
maxcens <- 8.4 # maximum censoring time in years
fac2x2design(n, rateC, hrA, hrB, hrAB, mincens, maxcens, dig = 2, alpha = 0.05)
$events
[1] 954.8738 # expected number of events
$evtprob # event probabilities for the C, A, B, and AB groups, respectively
probC probA probB probAB
0.2446365 0.2012540 0.2012540 0.1831806
$powerEA3overallA
[1] 0.5861992 # Equal Allocation 3's power to detect the overall A effect
$powerEA3simpleA
[1] 0.5817954 # Equal Allocation 3's power to detect the simple A effect
$powerEA3simplAB
[1] 0.9071236 # Equal Allocation 3's power to detect the simple AB effect
$powerEA3anyA
[1] 0.7060777 # Equal Allocation 3's power to detect either the overall A or simple A effects
$powerPA2overallA
[1] 0.6582819 # Proportional Allocation 2's power to detect the overall A effect
$powerPA2simpleAB
[1] 0.9197286 # Proportional Allocation 2's power to detect the simple AB effect
$powerEA2simpleA
[1] 0.6203837 # Equal Allocation 2's power to detect the simple A effect
$powerEA2simpleAB
[1] 0.9226679 # Equal Allocation 2's power to detect the simple AB effect
$powerA
[1] 0.7182932 # power to detect the overall A effect at the two-sided 0.05 level
```

Leifer, E.S., Troendle, J.F., Kolecki, A., Follmann, D. Joint testing of overall and simple effect for the two-by-two factorial design. 2020. Submitted.

Lin, D-Y., Gong, J., Gallo, P., et al. Simultaneous inference on treatment effects in survival studies with factorial designs. *Biometrics*. 2016; 72: 1078-1085.

Slud, E.V. Analysis of factorial survival experiments. *Biometrics*. 1994; 50: 25-38.